Can Labour win again? This month's Guardian/ICM poll suggests the answer is a cautious yes – but the party has yet to convince voters it has the right team and policies to run the country.

The impact of last year's defeat is still felt. The poll shows 69% of voters think the party has been damaged by the election and only 34% think it has the right policies to rescue the economy. A nation cooling on the coalition is yet to show enthusiasm for the alternative.

Guardian/ICM poll on voting intentions

Yet there are signs that Labour's position could begin to improve. The party may only be narrowly ahead of the Conservatives in ICM voting intention – although some other pollsters including online YouGov regularly find a bigger lead, with Labour above 40% – but the poll does find that 41% agree that Labour "has the right policies to appeal to someone like me" – one point ahead of the 40% who disagree.

By 10 points, 50% to 40%, voters also feel Labour "deserves another chance in government". It's true that figure includes 92% of people who already plan to vote Labour, but a decent chunk of people who voted Lib Dem in 2010 – 57% – think Labour deserves a second chance.

Wales – where 77% agree – and the north of England and Scotland – 60% – are particularly persuaded. Labour's future depends on winning more in the south, where 43% now think it deserves another spell in power.

Whether the party wins depends on its policies and its leaders. Here the picture is less encouraging. Even among definite Labour voters, only 68% are convinced by the party's economic plans – and among all voters that figure is 34%.

The poll shows almost two-to-one opposition to the speed of cuts, but that does not mean voters are yet persuaded there is an alternative.

Ahead of a conference in which Ed Miliband wants to signal a loosening of trade union power inside Labour, 47% think the party is still too close to unions. Among Labour voters, 37% think the same thing.

By contrast only 32% of all voters – and 44% of Labour ones – disagree with the statement "Labour is too tied to the trade unions".

Labour has other challenges. By eight points, 45% to 37%, people agree the party "has enough talented people to form a government". But only 30% agree it "has the right leader in Ed Miliband"; 48% who say the opposite. Even among definite Labour voters, only 49% say Miliband is the right leader, while 33% disagree and 15% express no view either way.

The Labour leader's approval rating is lower than those of David Cameron, Nick Clegg and George Osborne. He beats only Ed Balls.

Ratings have risen across the board since the summer. For Cameron, 49% think he is doing a good job (up 6), and 45% bad (down 3). For Osborne, 36% say good (up 2) and 42% bad (down 2). For Clegg, 39% say good (up 6) and 47% bad (down 7).

Among Labour politicians, 34% think Miliband is doing a good job (up 3) and 48% say bad (up 1). For shadow chancellor Ed Balls – not previously included in the survey – 27% say he is doing a good job and 45% bad.

Yet more voters would like to see Labour governing with a majority than any alternative. Asked to pick from a range of options, 27% say they would like a Labour government and a further 16% a Labour-Lib Dem coalition. Meanwhile 22% want to see the Conservatives on their own, and a further 16% a Conservative-Lib Dem coalition.

ICM Research interviewed a random sample of 1,003 adults aged 18+ by telephone on 20-21 September 2011. Interviews were conducted across the country and the results have been weighted to the profile of all adults. ICM is a member of the British Polling Council and abides by its rules.